David Cameron has urged British voters not to "roll the dice" on their children's futures by quitting the EU, as he delivered an impassioned warning that Brexit would cost economic growth and jobs.

The Prime Minister was repeatedly accused of "scaremongering" as he took questions from a live studio audience in the first major setpiece TV event of the referendum campaign.

But he insisted "this is not about scaring anybody", as he set out concerns that the UK would face barriers to trade with the 500 million-population European single market if it votes Leave on June 23.

Speaking on Sky News's EU: In or Out? broadcast, Mr Cameron accepted that levels of EU migration into the UK were "a challenge".

But he said he expected inward and outward migration to come back into balance as ailing continental economies start to catch up with the UK's "extraordinary" levels of job creation - though he did not give a timetable for this to happen.

It would be "madness" to try to cut numbers by "trashing our economy and pulling out of the single market", he warned.

Pro-Brexit former cabinet minster Iain Duncan Smith said it was "telling" that the PM refused to set any date for meeting his commitment to cut net migration - currently standing at 333,000 - to below 100,000.

"I thought that was a telling moment because he realised it is difficult to achieve that without coming out of the EU and close our borders," said the former work and pensions secretary.

Mr Cameron was challenged over immigration by retired NHS worker Alison Hyde-Chadwick, who demanded to know how the health service could be protected from "the seemingly never-ending stream of people from Europe".

And he was accused of "waffling" by student Soraya Bouazzaoui, as he tried to assure her that Turkey would not be joining the EU "in decades".

The PM said: "We are in a single market. It is a market of 500 million people. It is vital to the success of our businesses. Part of that single market is British people being able to work and live in other European countries and Europeans being able to live and work in our country.

"If you want to get out of the single market, which is what the Leave campaign want to do, you will fundamentally damage our economy. That cannot be the right way of controlling immigration. It would make our economy smaller, it would cost jobs, we would be poorer as a country.

"That would have a real effect on people watching this show - fewer jobs, we'd see prices go up because the pound would go down, the cost of the weekly shop would go up."

Leaving the single market would be an "act of economic self-harm" for the UK, and might mean its steel industry and car manufacturers facing tariffs to sell its products to Europe and its financial services sector seeing euro-linked business move to the continent, he said.

Small businessman James Dexter asked the PM what "personal damage the scaremongering has done to your legacy".

But Mr Cameron replied: "I don't accept it is scaremongering. I am genuinely worried about Britain leaving the single market."

He urged parents to think about their children's future when making the decision on June 23.

"I would just say to everybody: as we go home and wake up in the morning and look our children and our grandchildren in the eye and we think who we are responsible for through our pay packet, let us not roll the dice on their future.

"Britain doesn't succeed when we quit, we succeed when we get stuck in and we work to improve these organisations and we safeguard the prosperity and the security of this great country. To me, that's what it's all about."

Mr Cameron acknowledged frustrations with the way the EU worked, but insisted that it was better to work on the inside instead of being a "quitter".

Despite the potential risk of Brexit and the split within the Tory ranks, Mr Cameron said he was "delighted" to be holding the referendum and would "carry out the instructions of the British people".

And he hailed Boris Johnson as "a very talented guy" despite his bitter attacks on the Remain campaign, which have seen the former London mayor dismiss Mr Cameron's warnings as "nonsense". While declining to say whether he thought Johnson would make a good PM, he said the Leave campaign figurehead still had "plenty of fuel in the tank" and "a huge amount to give to public service".

The Prime Minister defended the Remain campaign's tactics - branded Project Fear by critics - including the use of a claim that the UK would be £4,300 a household worse off as a result of Brexit.

"That figure is the loss to the economy divided by the number of households in our country," he said.

"If our country is poorer, then our households are going to be poorer. What this means is fewer jobs, it means lower wages, it means less income.

"Those are the things that we would be inflicting on ourselves if we voted to leave."

He insisted he had never claimed there would be a world war if Britain left the EU, but added: "On our continent in the last century, twice we had an enormous bloodbath between our nations ... Can we be so confident that we have solved all of Europe's problems and all of Europe's tensions?"